References

POWER-EXPONENTIAL TRANSSERIES AS SOLUTIONS TO ODE


[1] A. D. Bruno, Asymptotic behaviour and expansions of solutions to an ordinary differential equation, Russian Mathem. Surveys 59(3) (2004), 429-480.
DOI: https://doi.org/10.1070/RM2004v059n03ABEH000736

[2] A. D. Bruno and N. A. Kudryashov, Expansions of solutions to the equation by algorithms of power geometry, Ukrainian Mathematical Bulletin 6(3) (2009), 311-337.

[3] A. D. Bruno, Exponential expansions of solutions to an ordinary differential equation, Doklady Mathematics 85(2) (2012), 259-264.
DOI: https://doi.org/10.1134/S1064562412020287

[4] G. A. Edgar, Transseries for Beginners, arXiv 0801.4877v5 (2009).
http://arxiv.org/abs/0801.4877v5

[5] J.-P. Ramis, Séries Divergentes et Théories Asymptotiques, Panoramas and Synthéses, Société Mathématique de France 121 (1993).

[6] J. Cano, On the series defined by differential equations, with an extension of the Puiseux polygon construction to these equations, Analysis 13(1-2) (1993), 103-119.
DOI: https://doi.org/10.1524/anly.1993.13.12.103

[7] O. Costin, Topological construction of transseries and introduction to generalized Borel summability, Contemporary Mathematics 373 (2005), 137-177.
DOI: http://dx.doi.org/10.1090/conm/373/06918

[8] J. Thomann, Resommation des series formelles, Numerische Mathematik 58(1) (1990), 503-535.
DOI: https://doi.org/10.1007/BF01385638

[9] A. D. Bruno, Complicated and exotic expansions of solutions to the Painlevé equations, in: Formal and Analytic Solutions of Differential Equations, G. Filipuk et al. (Editors), Springer Proceedings in Mathematics & Statistics, Springer, Heidelberg 256 (2018), 103-145.
DOI: https://doi.org/10.1007/978-3-319-99148-1_7

[10] M. Hazewinkel, Editor, Multinomial Coefficient, Encyclopedia of Mathematics, 2001.
http://www.encyclopediaofmath.org/index.php?title=p/m065320